Recent Evolution in the Theory of Magnetic Reconnection and Its Connection with Turbulence

The concept of reconnection is found in many fields of physics with the closest analogue to magnetic reconnection being the reconnection of vortex tubes in hydrodynamics. In plasmas, magnetic reconnection plays an important role in release of energy associated with the magnetic shear into particle energy. Although most studies to date have focused on 2D reconnection, the availability of 3D petascale kinetic simulations have brought the complexity of 3D reconnection to the forefront in collisionless reconnection studies. Here we briefly review the latest advances in 2D and compare and contrast the results with recent 3D studies that address role of anomalous transport in reconnection, effects of turbulence on the rate and structure, among others. Another outcome of recent research is the realization of a deeper link between turbulence and reconnection where the common denominator is the generic formation of electron scale sheets which dissipate the energy through reconnection. Finally, we close the review by listing some of the major outstanding problems in reconnection physics.     

Microphysics in Astrophysical Plasmas

Although macroscale features dominate astrophysical images and energetics, the physics is controlled through microscale transport processes (conduction, diffusion) that mediate the flow of mass, momentum, energy, and charge. These microphysical processes manifest themselves in key (all) boundary layers and also operate within the body of the plasma. Crucially, most plasmas of interest are rarefied to the extent that classical particle collision length- and time-scales are long. Collective plasma kinetic phenomena then serve to scatter or otherwise modify the particle distribution functions and in so-doing govern the transport at the microscale level. Thus collisionless plasmas are capable of supporting thin shocks, current sheets which may be prone to magnetic reconnection, and the dissipation of turbulence cascades at kinetic scales. This paper lays the foundation for the accompanying collection that explores the current state of knowledge in this subject. The richness of plasma kinetic phenomena brings with it a rich diversity of microphysics that does not always, if ever, simply mimic classical collision-dominated transport. This can couple the macro- and microscale physics in profound ways, and in ways which thus depend on the astrophysical context.     

Microphysics of Quasi-parallel Shocks in Collisionless Plasmas

Shocks in collisionless plasmas require dissipation mechanisms which couple fields and particles at scales much less than the conventional collisional mean free path. For quasi-parallel geometries, where the upstream magnetic field makes a small angle to the shock normal direction, wave-particle coupling produces a broad transition zone with large amplitude, nonlinear magnetic pulsations playing an important role. At high Mach numbers, ion reflection and acceleration are dominant processes which control the structure and dissipation at the shock. Accelerated particles produce a precursor, or foreshock, characterized by low frequency magnetic waves which are convected by the plasma flow into the shock transition zone. The interplay between energetic particles, waves, ion reflection and acceleration leads to a complicated interdependent system. This review discusses the spacecraft observations which have motivated the current view of the high Mach number quasi-parallel shock, and the theories and simulation studies which have led to a better understanding of the microphysics on which the quasi-parallel shock depends.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

Non-Linear Growth of Trapped Particle Modes in Linearly Stable, Current-Carrying Plasmas – A Fundamental Process in Plasma Turbulence and Anomalous Transport

The two-stream instability as a fundamental process in a current-carrying plasma is reconsidered. Its well-established linear version, based on kinetic Landau theory, predicts a threshold for the drift velocity between both species below which the plasma should be stable. We report on simulations which, however, show that a plasma as a non-linearly responding medium can be destabilized well below this threshold. Responsible for this unexpected behaviour are coherent, electrostatic, trapped particle structures such as phase space vortices or holes which can grow non-linearly out of thermal noise receiving their energy from the net imbalance of loss of electron kinetic energy and gain of ion kinetic energy. The birth of predominantly zero-energy holes is shown numerically being associated with initial, non-topological fluctuations. The latter are not subject to Landau damping, as they lie outside the realm of linear wave theory. For a pair plasma a typical scenario is presented, which encompasses several regimes such as non-linear growth of multiple holes, saturation and fully developed structural turbulence as well as an asymptotic approach to a new collisionless equilibrium. During the transient, structural state the plasma transport appears to be highly anomalous.     

Theory and Simulation of Reconnection

Reconnection is a major commonality of solar and magnetospheric physics. It was conjectured by Giovanelli in 1946 to explain particle acceleration in solar flares near magnetic neutral points. Since than it has been broadly applied in space physics including magnetospheric physics. In a special way this is due to Harry Petschek, who in 1994 published his ground breaking solution for a 2D magnetized plasma flow in regions containing singularities of vanishing magnetic field. Petschek’s reconnection theory was questioned in endless disputes and arguments, but his work stimulated the further investigation of this phenomenon like no other. However, there are questions left open. We consider two of them – “anomalous” resistivity in collisionless space plasma and the nature of reconnection in three dimensions. The CLUSTER and SOHO missions address these two aspects of reconnection in a complementary way -- the resistivity problem in situ in the magnetosphere and the 3D aspect by remote sensing of the Sun. We demonstrate that the search for answers to both questions leads beyond the applicability of analytical theories and that appropriate numerical approaches are necessary to investigate the essentially nonlinear and nonlocal processes involved. Necessary are both micro-physical, kinetic Vlasov-equation based methods of investigation as well as large scale (MHD) simulations to obtain the geometry and topology of the acting fields and flows.     

Coupling of macroscopic and small scale phenomena

Collisionless microscopic phenomena such as anomalous resistivity, particle acceleration and heat conduction have been successfully treated by particle simulations. Such simulations are usually restricted to volume elements and time scales that are small compared to global scales or even the space and time steps in macroscopic codes. Despite the recent code advances and increases in computing power, it remains necessary to determine the effect of macroscopic dynamics on small scale phenomena and vice versa. The sensitivity of microscopic simulation results to macroscopic boundary conditions is demonstrated. Macroscopic codes, on the other hand, are examined for their dependence on microscopic details. The consequences for the design and analysis of simulation experiments in space physics are discussed. Combining macroscopic and microscopic aspects in a single simulation, despite the usual disparity of scales, will remain a challenging problem.     

Magnetic Turbulence in the Geospace Environment

Magnetic turbulence is found in most space plasmas, including the Earth’s magnetosphere, and the interaction region between the magnetosphere and the solar wind. Recent spacecraft observations of magnetic turbulence in the ion foreshock, in the magnetosheath, in the polar cusp regions, in the magnetotail, and in the high latitude ionosphere are reviewed. It is found that: 1. A large share of magnetic turbulence in the geospace environment is generated locally, as due for instance to the reflected ion beams in the ion foreshock, to temperature anisotropy in the magnetosheath and the polar cusp regions, to velocity shear in the magnetosheath and magnetotail, and to magnetic reconnection at the magnetopause and in the magnetotail. 2. Spectral indices close to the Kolmogorov value can be recovered for low frequency turbulence when long enough intervals at relatively constant flow speed are analyzed in the magnetotail, or when fluctuations in the magnetosheath are considered far downstream from the bow shock. 3. For high frequency turbulence, a spectral index α?2.3 or larger is observed in most geospace regions, in agreement with what is observed in the solar wind. 4. More studies are needed to gain an understanding of turbulence dissipation in the geospace environment, also keeping in mind that the strong temperature anisotropies which are observed show that wave particle interactions can be a source of wave emission rather than of turbulence dissipation. 5. Several spacecraft observations show the existence of vortices in the magnetosheath, on the magnetopause, in the magnetotail, and in the ionosphere, so that they may have a primary role in the turbulent injection and evolution. The influence of such a turbulence on the plasma transport, dynamics, and energization will be described, also using the results of numerical simulations.     

Shock-wave structure in collisionless plasmas from results of laboratory experiments

Results of laboratory experiments on the study of collisionless shock wave structure in plasmas with and without a magnetic field are summarized, and comparisons with theoretical inferences are made. Consideration is given to the clarification of the collisionless dissipation mechanism and to the causes that bring it about. Transition conditions from one type of shock wave to another are analyzed. The relationship between laboratory experiments and the Earth bow shock measurements is also examined.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

Plasma kinetics in the solar wind

An account is given of the observations and theoretical ideas concerning the role of kinetic processes in the solar wind. This includes, first of all, the measurements on distribution functions of plasma electrons and protons, the relation of the observed non-thermal electron features with the concept of an exospheric expansion of the solar corona, and the connection of non-thermal proton distributions with bulk flow inhomogeneities of the wind. A discussion is given of the present understanding of the connection between observed features of the particle distributions and anomalous values of some plasma transport coefficients, which in turn determine the actual values of macroscopic plasma parameters.A further topic of the review is that of possible kinetic processes occurring within small scale structures in the solar wind, like collisionless shocks, various types of discontinuities and D-sheets.     

Dynamical Systems Approach to Space Environment Turbulence

Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach offers powerful mathematical and computational techniques to probe the origin and nature of space environment turbulence. Using the nonlinear dynamics tools such as the bifurcation diagram and Poincaré maps, we study the transition from order to chaos, from weak to strong chaos, and the destruction of a chaotic attractor. The characterization of the complex system dynamics of the space environment, such as the Alfvén turbulence, can improve the capability of monitoring Sun-Earth connections and prediction of space weather. This revised version was published online in August 2006 with corrections to the Cover Date.     

可压缩湍流的多尺度分析

作者的研究团队近几年在可压缩湍流的多尺度性质方面开展了系统的研究工作。通过多过程分解,研究了可压缩湍流中的速度和热力学量的剪切部分、胀压部分、伪声模态、声模态、熵模态的多尺度性质,并总结了各类可压缩条件下的速度和热力学量的谱的标度律。通过滤波方法,研究了动能和热力学量的多尺度传输现象,并重点分析了可压缩性对动能胀压部分的多尺度传输的影响。在可压缩均匀剪切湍流中,可压缩效应更加明显,可压缩湍动能和耗散率等物理量的马赫数标度率与各向同性湍流类似,但胀压分量所占比重更大,并且变形速度张量特征值的概率密度函数和流动拓扑结构的比例分布等统计量随马赫数的变化也更加明显。对于振动非平衡可压缩各向同性湍流,平动-转动内能模式和振动内能模式间的弛豫效应导致密度梯度与振动温度梯度方向的偏离,从而弱化了流场中压缩和膨胀运动对振动弛豫率的影响。化学反应放热会显著增加流场的压缩与膨胀运动,导致速度胀压分量和热力学量的能谱在所有尺度均增大,湍动能和耗散率的标度律表现出马赫数无关性。     

Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

Emerging Parameter Space Map of Magnetic Reconnection in Collisional and Kinetic Regimes

In large-scale systems of interest to solar physics, there is growing evidence that magnetic reconnection involves the formation of extended current sheets which are unstable to plasmoids (secondary magnetic islands). Recent results suggest that plasmoids may play a critical role in the evolution of reconnection, and have raised fundamental questions regarding the applicability of resistive MHD to various regimes. In collisional plasmas, where the thickness of all resistive layers remain larger than the ion gyroradius, simulations results indicate that plasmoids permit reconnection to proceed much faster than the slow Sweet-Parker scaling. However, it appears these rates are still a factor of ～10× slower than observed in kinetic regimes, where the diffusion region current sheet falls below the ion gyroradius and additional physics beyond MHD becomes crucially important. Over a broad range of interesting parameters, the formation of plasmoids may naturally induce a transition into these kinetic regimes. New insights into this scenario have emerged in recent years based on a combination of linear theory, fluid simulations and fully kinetic simulations which retain a Fokker-Planck collision operator to allow a rigorous treatment of Coulomb collisions as the reconnection electric field exceeds the runaway limit. Here, we present some new results from this approach for guide field reconnection. Based upon these results, a parameter space map is constructed that summarizes the present understanding of how reconnection proceeds in various regimes.     

Coherent nonlinear effects on electromagnetic wave-particle interactions

In many particle simulations and space experiments, the knowledge of nonlinear characteristics of both waves and particles in plasmas is very helpful in the data analysis phase. Such knowledge is needed even more in the designing phase of appropriate diagnostics and probings in both simulations and space experiments. In this tutorial lecture, I will attempt to provide a basic introduction to the fundamental features of coherent nonlinear wave-particle and wave-wave interactions in magnetized plasmas. The present lecture covers only some of the important and basic characteristics in the coherent nonlinear interactions. The main subjects are: (1) trapping dynamics in the electrostatic wave, (2) nonlinear phase trapping and phase bunching in electromagnetic wave both in homogeneous and inhomogeneous plasmas, and (3) coherent three wave interactions.     

Why space physics needs to go beyond the MHD box

Magnetohydrodynamic (MHD) theory has been used in space physics for more than forty years, yet many important questions about space plasmas remain unanswered. We still do not understand how the solar wind is accelerated, how mass, momentum and energy are transported into the magnetosphere and what mechanisms initiate substorms. Questions have been raised from the beginning of the space era whether MHD theory can describe correctly space plasmas that are collisionless and rarely in thermal equilibrium. Ideal MHD fluids do not induce electromotive force, hence they lose the capability to interact electromagnetically. No currents and magnetic fields are generated, rendering ideal MHD theory not very useful for space plasmas. Observations from the plasma sheet are used as examples to show how collisionless plasmas behave. Interpreting these observations using MHD and ideal MHD concepts can lead to misleading conclusions. Notably, the bursty bulk flows (BBF) with large mean velocities left(〈 v 〉≥400 km s right) that have been interpreted previously as E×B flows are shown to involve much more complicated physics. The sources of these nonvanishing 〈 v 〉 events, while still not known, are intimately related to mechanisms that create large phase space gradients that include beams and acceleration of ions to MeV energies. The distributions of these nonvanishing 〈 v 〉 events are associated with large amplitude variations of the magnetic field at frequencies up to and exceeding the local Larmor frequency where MHD theory is not valid. Understanding collisionless plasma dynamics such as substorms in the plasma sheet requires the self-consistency that only kinetic theory can provide. Kinetic modeling is still undergoing continual development with many studies limited to one and two dimensions, but there is urgent need to improve these models as more and more data show kinetic physics is fundamentally important. Only then will we be able to make progress and obtain a correct picture of how collisionless plasmas work in space.     

The Dynamic Quasiperpendicular Shock: Cluster Discoveries

The physics of collisionless shocks is a very broad topic which has been studied for more than five decades. However, there are a number of important issues which remain unresolved. The energy repartition amongst particle populations in quasiperpendicular shocks is a multi-scale process related to the spatial and temporal structure of the electromagnetic fields within the shock layer. The most important processes take place in the close vicinity of the major magnetic transition or ramp region. The distribution of electromagnetic fields in this region determines the characteristics of ion reflection and thus defines the conditions for ion heating and energy dissipation for supercritical shocks and also the region where an important part of electron heating takes place. In other words, the ramp region determines the main characteristics of energy repartition. All these processes are crucially dependent upon the characteristic spatial scales of the ramp and foot region provided that the shock is stationary. The process of shock formation consists of the steepening of a large amplitude nonlinear wave. At some point in its evolution the steepening is arrested by processes occurring within the shock transition. From the earliest studies of collisionless shocks these processes were identified as nonlinearity, dissipation, and dispersion. Their relative role determines the scales of electric and magnetic fields, and so control the characteristics of processes such as ion reflection, electron heating and particle acceleration. The determination of the scales of the electric and magnetic field is one of the key issues in the physics of collisionless shocks. Moreover, it is well known that under certain conditions shocks manifest a nonstationary dynamic behaviour called reformation. It was suggested that the transition from stationary to nonstationary quasiperiodic dynamics is related to gradients, e.g. scales of the ramp region and its associated whistler waves that form a precursor wave train. This implies that the ramp region should be considered as the source of these waves. All these questions have been studied making use observations from the Cluster satellites. The Cluster project continues to provide a unique viewpoint from which to study the scales of shocks. During its lifetime the inter-satellite distance between the Cluster satellites has varied from 100 km to 10000 km allowing scientists to use the data best adapted for the given scientific objective. The purpose of this review is to address a subset of unresolved problems in collisionless shock physics from experimental point of view making use multi-point observations onboard Cluster satellites. The problems we address are determination of scales of fields and of a scale of electron heating, identification of energy source of precursor wave train, an estimate of the role of anomalous resistivity in energy dissipation process by means of measuring short scale wave fields, and direct observation of reformation process during one single shock front crossing.